Atomicity of lattice effect algebras and their sub-lattice effect algebras

Jan Paseka; Zdena Riečanová

Kybernetika (2009)

  • Volume: 45, Issue: 6, page 1040-1051
  • ISSN: 0023-5954

Abstract

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We show some families of lattice effect algebras (a common generalization of orthomodular lattices and MV-effect algebras) each element E of which has atomic center C(E) or the subset S(E) of all sharp elements, resp. the center of compatibility B(E) or every block M of E. The atomicity of E or its sub-lattice effect algebras C(E), S(E), B(E) and blocks M of E is very useful equipment for the investigations of its algebraic and topological properties, the existence or smearing of states on E, questions about isomorphisms and so. Namely we touch the families of complete lattice effect algebras, or lattice effect algebras with finitely many blocks, or complete atomic lattice effect algebra E with Hausdorff interval topology.

How to cite

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Paseka, Jan, and Riečanová, Zdena. "Atomicity of lattice effect algebras and their sub-lattice effect algebras." Kybernetika 45.6 (2009): 1040-1051. <http://eudml.org/doc/37683>.

@article{Paseka2009,
abstract = {We show some families of lattice effect algebras (a common generalization of orthomodular lattices and MV-effect algebras) each element E of which has atomic center C(E) or the subset S(E) of all sharp elements, resp. the center of compatibility B(E) or every block M of E. The atomicity of E or its sub-lattice effect algebras C(E), S(E), B(E) and blocks M of E is very useful equipment for the investigations of its algebraic and topological properties, the existence or smearing of states on E, questions about isomorphisms and so. Namely we touch the families of complete lattice effect algebras, or lattice effect algebras with finitely many blocks, or complete atomic lattice effect algebra E with Hausdorff interval topology.},
author = {Paseka, Jan, Riečanová, Zdena},
journal = {Kybernetika},
keywords = {non-classical logics; D-posets; effect algebras; MV-algebras; atomicity; MV-algebras; effect algebras; D-posets; atomicity},
language = {eng},
number = {6},
pages = {1040-1051},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Atomicity of lattice effect algebras and their sub-lattice effect algebras},
url = {http://eudml.org/doc/37683},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Paseka, Jan
AU - Riečanová, Zdena
TI - Atomicity of lattice effect algebras and their sub-lattice effect algebras
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 6
SP - 1040
EP - 1051
AB - We show some families of lattice effect algebras (a common generalization of orthomodular lattices and MV-effect algebras) each element E of which has atomic center C(E) or the subset S(E) of all sharp elements, resp. the center of compatibility B(E) or every block M of E. The atomicity of E or its sub-lattice effect algebras C(E), S(E), B(E) and blocks M of E is very useful equipment for the investigations of its algebraic and topological properties, the existence or smearing of states on E, questions about isomorphisms and so. Namely we touch the families of complete lattice effect algebras, or lattice effect algebras with finitely many blocks, or complete atomic lattice effect algebra E with Hausdorff interval topology.
LA - eng
KW - non-classical logics; D-posets; effect algebras; MV-algebras; atomicity; MV-algebras; effect algebras; D-posets; atomicity
UR - http://eudml.org/doc/37683
ER -

References

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